Analytical determination of the PBH formation collapse efficiency

Develop a fully analytical understanding of the collapse-efficiency parameter values for primordial black-hole formation, particularly during the post-inflationary epoch.

Background

The paper parametrizes the initial primordial-black-hole mass as a fraction of the horizon mass, where is the collapse-efficiency parameter. The authors note that more accurate numerical methods can incorporate the cosmological background and scalar-perturbation profile when estimating this formation mass. However, they identify the lack of a fully analytical determination of , especially for primordial black holes forming after inflation, as an unresolved issue. This is relevant because the paper’s critical runaway conditions depend directly on the initial mass and therefore on the assumed collapse efficiency.

References

However, a fully analytical understanding of the values of \gamma, particularly in the context of PBH formation during the post-inflationary epoch is still lacking.

— PBH runaway during reheating  (2609.10696 - Haque et al., 9 Sep 2026) in Footnote following Eq. (2), Section 2.1, “Absorption and evaporation”